Escape of a Uniform Random Walk from an Interval
Data Analysis, Statistics and Probability
2007-05-23 v1 Statistical Mechanics
Abstract
We study the first-passage properties of a random walk in the unit interval in which the length of a single step is uniformly distributed over the finite range [-a,a]. For a of the order of one, the exit probabilities to each edge of the interval and the exit time from the interval exhibit anomalous properties stemming from the change in the minimum number of steps to escape the interval as a function of the starting point. As a decreases, first-passage properties approach those of continuum diffusion, but non-diffusive effects remain because of residual discreteness effects
Keywords
Cite
@article{arxiv.physics/0512221,
title = {Escape of a Uniform Random Walk from an Interval},
author = {T. Antal and S. Redner},
journal= {arXiv preprint arXiv:physics/0512221},
year = {2007}
}
Comments
8 pages, 8 figures, 2 column revtex4 format